Mathematically equivalent expert-reduction orders can produce observably different sparse-MoE executions. We isolate this effect in native DeepSeek-V4-Flash by freezing local MoE state and varying only aggregation semantics. Four schemes separate operand representation from accumulator precision. At one layer-5 fork, 720 A-mode orders yield 10 continuation basins; 720 B-mode orders form 360 exact structural classes and 11 basins. Under one Chinese prompt, the B classes split into 202 layoffs, 113 hiring, and 45 other continuations. Maximum-L-infinity B-branch selection separates 12, 24, and 36 of 50 prompts by 8, 16, and 32 tokens. Across 192 persistent trajectories per scheme, P32, A, and B change every native-reference route trajectory, while C preserves routes, token sequences, and texts. A separate 192-trajectory C check matches native MoE, post-mHC, next-router, and LM states bitwise. For one controlled B branch, exact post-mHC endpoint reconstruction reproduces the measured downstream trajectory. At the next decode boundary, exact FP64 reconstruction of the branch's full persistent state yields agreement for 301 downstream post-mHC states, 301 persistent-state checkpoints, 301 routes, predictions, and text over seven steps, given the same naturally generated next input. These controls identify post-mHC as an intra-token boundary and full persistent state as a cross-token continuation boundary. Identical tokens need not imply identical autoregressive state: divergence can survive a token boundary and become visible later. These results make expert operand conversion, accumulator precision, and reduction order part of a numerical compatibility contract for sparse-MoE runtimes and hardware backends. They establish controlled causal possibility, not deployment incidence; C's order invariance is limited to evaluated six-term states and schedules.
Direct low-precision write-back can erase nonzero optimizer proposals. We ask what a high-precision reference trace establishes before a low-precision run. The exact target-code event is auditable coordinatewise on a realized target trajectory; pre-run aggregate projection also assumes the reference remains a useful counterfactual. In a controlled two-layer grid, 55/72 cells have measured and predicted post-initialization crossings: times span $384\times$, 52/55 are within 15\%, and 4/72 differ in category. Matched decoder experiments show stochastic rather than nearest write-back recovers most of the loss gap. A prospective analytic-grid E4M3 audit reuses one fp32 trace across three unseen NeoX-style seeds. It passes absolute-accuracy and skill gates (macro RMSE 0.00858) but fails directional specificity. In a target-outcome-blind comparison, a historical template has lower descriptive RMSE (0.00360) than the predeclared source predictor (0.00438); a post-outcome decomposition assigns 99.65\% of variation to common time, while a privileged matched-reference correction reaches 0.00283. Persistent-native Study~1 pairs three seeds across two schedules. Five cells are canonical; a manual sixth lacks canonical process identity, so the registered result remains inconclusive. A retrospective protocol-deviation analysis is negative because the complete constant-mid cohort is disjoint from the recovered cosine-restart cell. Study~2 reports mean full-SR/dead-zone-SR recoveries of 0.9766/0.9777 and a ratio of 1.0012, a policy contrast rather than causal mediation. Simulated-INT3 Study~3 replays six checkpoints and observes a 7.3071-nat (69.71\%) validation-loss reduction in one fixed seed. Exact events and write-back effects are auditable, but aggregate forecasts can reflect shared time rather than source-specific transfer.